Full rank distance codes and optimal STBC for BPSK modulation

Viewing the codewords of an [n, k] linear code over a field F(q^m) as m×n matrices over F_q by expanding each entry of the codeword with respect to an F_q-basis of F(q^m), the rank weight of a codeword is the rank over F_q of the corresponding matrix and the rank of the code is the minimum rank weight among all non-zero codewords. For m≥n-k+1, codes with maximum possible rank distance, called maximum rank distance (MRD) codes have been studied previously. We study codes with maximum possible rank distance for the cases m≤n-k+1, calling them full rank distance (FRD) codes. Generator matrices of FRD codes are characterized.